Random Area and Perimeter
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Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ and $L$.
Will it just be $$f(x,y) = 2xy(x+y)$$
The above is just my guess and likely wrong, because when I use it to calculate $mathbb{E}(A)$ and $mathbb{E}(L)$ , I get the wrong values, so what will be the distribution function?
probability probability-distributions random-variables uniform-distribution expected-value
asked Dec 3 '18 at 13:38
user601297user601297
39219
$endgroup$
add a comment |
$begingroup$
Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ and $L$.
Will it just be $$f(x,y) = 2xy(x+y)$$
The above is just my guess and likely wrong, because when I use it to calculate $mathbb{E}(A)$ and $mathbb{E}(L)$ , I get the wrong values, so what will be the distribution function?
probability probability-distributions random-variables uniform-distribution expected-value
asked Dec 3 '18 at 13:38
user601297user601297
39219
$endgroup$
$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
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You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05
add a comment |
$begingroup$
Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ and $L$.
Will it just be $$f(x,y) = 2xy(x+y)$$
The above is just my guess and likely wrong, because when I use it to calculate $mathbb{E}(A)$ and $mathbb{E}(L)$ , I get the wrong values, so what will be the distribution function?
probability probability-distributions random-variables uniform-distribution expected-value
asked Dec 3 '18 at 13:38
user601297user601297
39219
$endgroup$
Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ and $L$.
Will it just be $$f(x,y) = 2xy(x+y)$$
The above is just my guess and likely wrong, because when I use it to calculate $mathbb{E}(A)$ and $mathbb{E}(L)$ , I get the wrong values, so what will be the distribution function?
probability probability-distributions random-variables uniform-distribution expected-value
probability probability-distributions random-variables uniform-distribution expected-value
asked Dec 3 '18 at 13:38
user601297user601297
39219
asked Dec 3 '18 at 13:38
user601297user601297
39219
asked Dec 3 '18 at 13:38
user601297user601297
39219
asked Dec 3 '18 at 13:38
user601297user601297
39219
asked Dec 3 '18 at 13:38
user601297user601297
39219
39219
$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
$begingroup$
You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05
add a comment |
$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
$begingroup$
You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05
$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
$begingroup$
You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05
add a comment |
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$begingroup$
area is a product of two uniform random variable. see answers of this question. perimeter is twice the sum of two uniform random variable. Its PDF is a triangular shaped function.
$endgroup$
– achille hui
Dec 3 '18 at 13:58
$begingroup$
You do not need to find the joint density (which is what your $f$ looks like), and this is pretty hard to do.
$endgroup$
– Mike Earnest
Dec 3 '18 at 15:58
$begingroup$
Ok, I think I interpreted the question wrong
$endgroup$
– user601297
Dec 3 '18 at 20:05